Amazon.com Inc. is exploring an ambitious offensive aimed at infiltrating the last bastion of traditional pay-television: live sports.In recent months, the e-commerce giant has been in talks for live game rights with heavy-hitters like the National Basketball Association, Major League Baseball and the National Football League, as well as smaller players like Major League Soccer, the Atlantic Coast Conference, college sports network Campus Insiders, 120 Sports, National Lacrosse League, Major League Lacrosse and World Surf League, the people said.With at least some leagues, including the NBA, Amazon has floated creating a premium, exclusive sports package that would accompany a Prime membership, though the details are unclear, the people said. A premium sports package could entice new subscribers to Prime and to Amazon’s potential “skinny bundle” of live channels online.Amazon executives have even canvassed traditional TV networks for game rights they aren’t using. They have asked if Univision Communications Inc. would consider producing and packaging the extra Mexican soccer league games that it has rights to but doesn’t air, one of the people said. And they approached Walt Disney Co.’s ESPN and ONE World Sports, which airs offbeat sports like Russian hockey league matches, to seek leftover, unproduced live games, other people said.Amazon also is scouting abroad, on the cusp of a global video expansion. It paid $10,000 for a tender document to potentially bid on the popular Indian Premier League cricket games. And it is discussing licensing an international package of NBA games, a person familiar with the talks said.“My sense is they are interested in anything that might be out there,” said Chad Swofford, vice president of digital for the ACC, a college sports conference.An Amazon spokeswoman declined to comment on its sports efforts.Amazon’s potential entry into sports broadcasting could shake up a lucrative business that has long been a stronghold of traditional pay-television. That is in part because “they take such a view of the long game, while near-term financial returns drive the agenda for most companies,” one senior sports executive said. Amazon executives are keenly aware that the premium NFL Sunday Ticket package of afternoon football helped DirecTV acquire subscribers when it launched as a new rival to cable, people familiar with their thinking say.Amazon even asked to exclusively license the NBA’s League Pass, which offers live out-of-market games, one of the people said, but the NBA demurred, having long preferred selling it through many outlets.Amazon also is seeking sports packages like NFL Game Pass, which shows replays of matchups, to sell to Prime members as add-on channels, the people said.Leading the talks is Amazon’s head of sports, James DeLorenzo, a former Sports Illustrated executive hired in March. Also on Amazon’s acquisition team: Sunil Dave, a former Dish Network Corp.executive who negotiated with sports networks.Amazon is racing to compete against rival tech giants like Facebookand Twitter, as well as BAMTech, the spinoff of Major League Baseball, which are seeking sports rights to beef up their video offerings.One big hurdle: many premium rights are tied up. The NBA’s deal with ESPN and TNT stretches until the 2024-2025 season, while the NFL’s pacts with ESPN, CBS, Fox and NBC run through early next decade. Many college conferences’ rights lie with various TV networks. And Disney’s recent investment in BAMTech means ESPN’s extra sports rights likely will land in its forthcoming multisport streaming service with BAMTech, one person familiar with ESPN’s thinking said.Amazon has the firepower and willingness to bid for top-tier, exclusive sports rights when they become available, people familiar with its thinking say. Coming up next year: the NFL-Twitter deal for streaming 10 games. Amazon had bid for those rights this year, a person familiar with the matter said.Amazon would be wagering that sports will attract enough new Prime members to offset potentially large yearslong costs. Rival Netflix Inc. has long said viewers don’t care to watch sports on-demand after the fact, making it an unattractive investment compared with shows or movies. Already, Amazon’s ballooning investments in video are a drag on its meager profits.The company may first grab a toehold in the “long tail” of sports, like lacrosse, gymnastics or surfing, sports executives say. Amazon executives believe the e-commerce giant can uniquely target a lacrosse viewer with lacrosse gear, for instance, allowing Amazon to land a greater return on a sports investment.“Amazon’s ability to aggregate information about individual consumers is without peer,” said Alexander Brown, chief executive of TV network ONE World Sports.The ability to re-target consumers could be key to justifying expensive sports rights as traditional networks grapple withdeclining ratings for some events, like NFL games this season.It isn’t uncommon for Amazon to float various ideas and retreat—a potential outcome of its sports foray as well, media executives cautioned. At times there are several overlapping video efforts going on at once—a model that Amazon Chief Executive Jeff Bezosencourages for a bit of “business Darwinism,” one person close to Amazon said.There is debate internally about whether a sports package should be available free with Prime or as a premium add-on subscription, the people said. It is still possible Amazon may just opt to license channels, like traditional cable distributors do, rather than acquire sports rights.SHALINI RAMACHANDRAN/Wall Street Journal